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PHASE Diagram & PHASE RULE PHASE DIaGRAM & PHASE RULE MATERIAL SC (MM1101) ASSIGNMENT Submitted to - Dr. Ranjit Prasad Presented by :- Shashank Karan : 2020UGCS023 Akhilesh Kumar Mishra : 2020UGCS053 Harsh Bajaj : 2020UGCS083 Ravi Kumar : 2020UGCS113 INTRODUCTION Before, dip diving into the topic lets first know what is PHASE ? ¤ A phase can be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics i.e. it is a physically distinct from other phases, chemically homogeneous and mechanically separable portion of a system. For example Let consider H₂O : it exsits as ice in solid , water as liquid and vapour as a gas . ¤ Different phases or of same phase of different component can be mixed to form another substance with unique property these are called solution or mixture . These can liquid-liquid, liquid-solid, liquid-gas, solid-solid , solid-liquid, solid-gas, gas- liquid , gas-gas and gas-solid composition. A solution (liquid or solid) is phase with more than one component; a mixture is a material with more than one phase Here in the given chapter we would be discussing about the phase change , their transformation , their kinetics the set of rules describing their changes and ultimately going through one Phase Diagram of Iron- carbon System. INTRODUCTION TO PHASE DIAGRAM A diagram that depicts existence of different phases of a system under equilibrium is termed as Phase Diagram. ¤ It is actually a collection of solubility limit curves. It is also known as equilibrium or constitutional diagram. ¤ Equilibrium phase diagrams represent the relationships between temperature, compositions and the quantities of phases at equilibrium. ¤ These diagrams do not indicate the dynamics when one phase transforms into another. ¤ Useful terminology related to phase diagrams: liquidus, solidus, solvus, terminal solid solution, invariant reaction, , inter-metallic compound, etc. ¤ Phase diagrams are classified according to the number of component present in a particular system. Here is the naming, we will be discussing it later. Single Component System – Unary Phase Diagram Two Component System – Binary Phase Diagram Three Component System – Tertiary Phase Diagram Four Component System – Quarter Phase Diagram IMPORTANT TERMINOLOGY AND SOME FEATURES OF A PHASE DIAGRAM 1. LIQUIDUS -– The liquidus is the temperature at which an alloy is completely melted. 2. SOLIDUS - The solidus is the highest temperature at which an alloy is solid. 3.Terminal Solid Solution - Solid phases (α and β) that exist near the ends of phase diagrams are called terminal solid solutions . 4.Invariant Reaction Reaction that occurs under equilibrium conditions at a specific temperature and specific composition which can not be varied. Important information, useful in materials development and selection, obtainable from a phase diagram: - It shows phases present at different compositions and temperatures under slow cooling (equilibrium) conditions. - It indicates equilibrium solid solubility of one element/compound in another. - It suggests temperature at which an alloy starts to solidify and the range of solidification. - It signals the temperature at which different phases start to melt. - Amount of each phase in a two-phase mixture can be obtained. Unary phase diagram If a system consists of just one component (e.g.: water), equilibrium of phases exist is depicted by unary phase diagram. The component may exist in different forms, thus variables here are – temperature and pressure. BINARY PHASE DIAGRAM If a system consists of two components, equilibrium of phases exist is depicted by binary phase diagram. For most systems, pressure is constant, thus independently variable parameters are – temperature and composition. Two components can be either two metals (Cu and Ni), or a metal and a compound (Fe and Fe3C), or two compounds (Al2O3 and Si2O3), etc. Two component systems are classified based on extent of mutual solid solubility – (a) completely soluble in both liquid and solid phases (isomorphous system) and (b) completely soluble in liquid phase whereas solubility is limited in solid state. For isomorphous system - E.g.: Cu-Ni, Ag-Au, Ge-Si , Al2O3,etc. GIBBS’S PHASE RULE In 1875, Josiah Williard Gibbs published a general principle governing systems in the thermodynamic equilibrium called the Phase Rule in a paper tilted on the Equilibrium of Heterogeneous Substances . “In a system under a set of conditions, number of phases (P) exist can be related to the number of components (C) and degrees of freedom (F)” by Gibbs phase rule. Where , Degrees of freedom refers to the number of independent variables (e.g.: pressure, temperature) that can be varied individually to effect changes in a system. Thermodynamically derived Gibbs phase rule: P+F = C+2 In practical conditions for metallurgical and materials systems, pressure can be treated as a constant (1 atm.). Thus Condensed Gibbs phase rule is written as: P+F = C+1 Hume-Ruthery conditions Hume-Rothery rules, named after William Hume-Rothery, are a set of basic rules that describe the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules; one refers to substitutional solid solutions, and the other refers to interstitial solid solutions. For substitutional solid solutions, the Hume-Rothery rules are as follows: 1. The atomic radius of the solute and solvent atoms must differ by no more than 15% ( ) ( ) %difference = x 100% ( ) 2. The crystal structures of solute and solvent must be similar. 3. Complete solubility occurs when the solvent and solute have the same valency. A metal is more likely to dissolve a metal of higher valency, than vice versa. 4. The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals tend to form intermetallic compounds instead of solid solutions. For interstitial solid solutions, the Hume-Rothery Rules are: 1. Solute atoms should have a smaller radius than 59% of the radius of solvent atoms. 2. The solute and solvent should have similar electronegativity. 3. Valency factor: two elements should have the same valence. The greater the difference in valence between solute and solvent atoms, the lower the solubility. Fundamentally these are restricted to binary systems that form either substitutional or interstitial solid solutions. However, this approach limits assessing advanced alloys which are commonly multicomponent systems. Free energy diagrams (or phase diagrams) offer in-depth knowledge of equilibrium restraints in complex systems. LEVER’S RULE The lever rule is a rule used to determine the mole fraction (xi) or the mass fraction (wi) of each phase of a binary equilibrium phase diagram. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line In an alloy or a mixture with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the mass fraction of the α phase is a B a w = ( wb-wb ) /( wb ) where a ● wb is the mass fraction of element B in the a phase b ● wb is the mass fraction of element B in the β phase ● wb is the mass fraction of element B in the entire alloy or mixture all at some fixed temperature or pressure. Procedure to find equilibrium relative amounts of phases (lever rule): - A tie-line is constructed across the two phase region at the temperature of the alloy to intersect the region boundaries. The relative amount of a phase is computed by taking the length of tie line from overall composition to the phase boundary for the other phase, and dividing by the total tieline length. In previous figure, relative amount of liquid and solid phases is given respectively by: VARIENT REACTIONS Observed triple point in unary phase diagram for water? How about eutectic point in binary phase diagram? These points are specific in the sense that they occur only at that particular conditions of concentration, temperature, pressure etc. Try changing any of the variable, it does not exist i.e. phases are not equilibrium any more! Hence they are known as invariant points, and represents invariant reactions. Invariant reactions result in different product phases: terminal phases and intermediate phases. Intermediate phases are either of varying composition (intermediate solid solution) or fixed composition (intermetallic compound). Occurrence of intermediate phases cannot be readily predicted from the nature of the pure components! Inter-metallic compounds differ from other chemical compounds in that the bonding is primarily metallic rather than ionic or covalent. E.g.: Fe3C is metallic, whereas MgO is covalent. When using the lever rules, inter-metallic compounds are treated like any other phase. Fe-C binary system – Phase transformations Fe-Fe3C phase diagram is characterized by five individual phases,: α–ferrite (BCC) Fe-C solid solution, γ-austenite (FCC) Fe-C solid solution, δ-ferrite (BCC) Fe-C solid solution, Fe3C (iron carbide) or cementite - an inter-metallic compound and liquid Fe-C solution and four invariant reactions: - peritectic reaction at 1495 C and 0.16%C, δ-ferrite + L ↔ γ-iron (austenite) - monotectic reaction 1495 C and 0.51%C, L ↔ L + γ-iron (austenite) - eutectic reaction at 1147 C and 4.3 %C, L ↔ γ-iron + Fe3C (cementite) [ledeburite] - eutectoid reaction at 723 C and 0.8%C, γ-iron ↔ α– ferrite + Fe3C (cementite) [pearlite] Fe-C alloys CLASSIFICATION Fe-C alloys are classified according to wt.% C present in the alloy for technological convenience as follows: Commercial pure irons % C < 0.008 Low-carbon/mild steels 0.008 - %C - 0.3 Medium carbon steels 0.3 - %C - 0.8 High-carbon steels 0.8- %C - 2.11 Cast irons 2.11 < %C Cast irons that were slowly cooled to room temperature consists of cementite, look whitish – white cast iron. If it contains graphite, look grayish – gray cast iron. It is heat treated to have graphite in form of nodules – malleable cast iron.
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